Firing patterns in the adaptive exponential integrate-and-fire model

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.

NineML: the network interchange for neuroscience modeling language

Sean Lewis Hill, Michael Lee Hines, Eilif Benjamin Muller

The growing number of large-scale neuronal network models has created a need for standards and guidelines to ease model sharing and facilitate the replication of results across different simulators. To foster community efforts towards such standards, the International Neuroinformatics Coordinating Facility (INCF) has formed its Multiscale Modeling program, and has assembled a task force of simulator developers to propose a declarative computer language for descriptions of large-scale neuronal networks. The name of the proposed language is "Network Interchange for Neuroscience Modeling Language" (NineML) and its initial focus is restricted to point neuron models. The INCF Multiscale Modeling task force has identified the key concepts of network modeling to be 1) spiking neurons 2) synapses 3) populations of neurons and 4) connectivity patterns across populations of neurons. Accordingly, the definition of NineML includes a set of mathematical abstractions to represent these concepts. NineML aims to provide tool support for explicit declarative definition of spiking neuronal network models both conceptually and mathematically in a simulator independent manner. In addition, NineML is designed to be self-consistent and highly flexible, allowing addition of new models and mathematical descriptions without modification of the previous structure and organization of the language. To achieve these goals, the language is being iteratively designed using several representative models with various levels of complexity as test cases. The design of NineML is divided in two semantic layers: the Abstraction Layer, which consists of core mathematical concepts necessary to express neuronal and synaptic dynamics and network connectivity patterns, and the User Layer, which provides constructs to specify the instantiation of a network model in terms that are familiar to computational neuroscience modelers. As part of the Abstraction Layer, NineML includes a flexible block diagram notation for describing spiking dynamics. The notation represents continuous and discrete variables, their evolution according to a set of rules such as a system of ordinary differential equations, and the conditions that induce a regime change, such as the transition from subthreshold mode to spiking and refractory modes. The User Layer provides syntax for specifying the structure of the elements of a spiking neuronal network. This includes parameters for each of the individual elements (cells, synapses, inputs) and the grouping of these entities into networks. In addition, the user layer defines the syntax for supplying parameter values to abstract connectivity patterns. The NineML specification is defined as an implementation-neutral object model representing all the concepts in the User and Abstraction Layers. Libraries for creating, manipulating, querying and serializing the NineML object model to a standard XML representation will be delivered for a variety of languages. The first priority of the task force is to deliver a publicly available Python implementation to support the wide range of simulators which provide a Python user interface (NEURON, NEST, Brian, MOOSE, GENESIS-3, PCSIM, PyNN, etc.). These libraries will allow simulator developers to quickly add support for NineML, and will thus catalyze the emergence of a broad software ecosystem supporting model definition interoperability around NineML.

2011

Computational fluid dynamics for naval engineering problems

Nicola Parolini

The subject of this thesis is the numerical simulation of viscous free-surface flows in naval engineering applications. State-of-the-art numerical methods based on the solution of the Navier-Stokes equations are used to predict the flow around different classes of boats. We investigate the role of the Computational Fluid Dynamics in the design of racing boats, such as America's Cup yachts and Olympic class rowing hull. The mathematical models describing the different aspects of the physical problem, as well as the numerical methods adopted for their solution, are introduced and critically discussed. The different phases of the overall numerical simulation procedure, from grid generation through the solution of the flow equations to the post-processing of the results, are described. We present the numerical simulations that have been performed to investigate the role of different design parameters in the conception of America's Cup yachts and we describe how the results obtained from the simulations are integrated into the overall design process. The free-surface flow around an Olympic rowing boat is also considered. We propose a simplified approach to take into account the effect of the boat dynamics in the prediction of the hydrodynamic forces acting on the boat. Based on the results of the simulations, we propose a new design concept and we investigate its potential benefits on the boat performances. One of the aspects that is found to be not completely satisfactory, within the standard numerical methods adopted, is the modelling of complex free-surface flows. The second part of this thesis is devoted to a more theoretical and methodological investigation of this aspect. In particular, we present and analyse a new numerical method based on the level set approach for the solution of two-fluid flows. The numerical scheme based on a finite element discretization is introduced and different critical aspects of its implementation are discussed. In particular, we present and analyse a new technique for the stabilization of the advection equation associated to the level set problem. Moreover, we propose a new reinitialization procedure for the level set function which plays a crucial role in the accuracy of the algorithm. The convergence properties of this procedure are analysed and comparisons with more standard approaches are presented. Finally, the proposed method has been used to solve a variety of test cases concerning time dependent two-fluid viscous flows. The results of the simulation are presented and discussed.

EPFL2004

NineML: the network interchange for neuroscience modeling language

Sean Lewis Hill, Michael Lee Hines, Eilif Benjamin Muller

2011

Computational fluid dynamics for naval engineering problems

Nicola Parolini

EPFL2004